#814485 (C++17) No.2122 黄金比で擬似乱数生成

提出ソース

結果

問題	No.2122 黄金比で擬似乱数生成
ユーザー	FF256grhy
提出日時	2022-11-04 23:59:03
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	10,397 bytes
コンパイル時間	2,296 ms
コンパイル使用メモリ	223,000 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-07-18 22:13:01
合計ジャッジ時間	3,056 ms
ジャッジサーバーID （参考情報）	judge1 / judge5

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	2 ms 5,376 KB
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	2 ms 5,376 KB
testcase_14	AC	2 ms 5,376 KB
testcase_15	AC	2 ms 5,376 KB
testcase_16	AC	2 ms 5,376 KB
testcase_17	AC	1 ms 5,376 KB
testcase_18	AC	2 ms 5,376 KB
testcase_19	AC	1 ms 5,376 KB
testcase_20	AC	1 ms 5,376 KB
testcase_21	AC	2 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	2 ms 5,376 KB
testcase_24	AC	1 ms 5,376 KB
testcase_25	AC	1 ms 5,376 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
#define incII(i, l, r) for(decay_t<decltype(r)> i = (l)    ; i <= (r); i++)
#define incIX(i, l, r) for(decay_t<decltype(r)> i = (l)    ; i <  (r); i++)
#define incXI(i, l, r) for(decay_t<decltype(r)> i = (l) + 1; i <= (r); i++)
#define incXX(i, l, r) for(decay_t<decltype(r)> i = (l) + 1; i <  (r); i++)
#define decII(i, l, r) for(decay_t<decltype(r)> i = (r)    ; i >= (l); i--)
#define decIX(i, l, r) for(decay_t<decltype(r)> i = (r) - 1; i >= (l); i--)
#define decXI(i, l, r) for(decay_t<decltype(r)> i = (r)    ; i >  (l); i--)
#define decXX(i, l, r) for(decay_t<decltype(r)> i = (r) - 1; i >  (l); i--)
#define inc(i, n)  incIX(i, 0, n)
#define dec(i, n)  decIX(i, 0, n)
#define inc1(i, n) incII(i, 1, n)
#define dec1(i, n) decII(i, 1, n)
auto inII = [](auto a, auto l, auto r) -> bool { return (l <= a && a <= r); };
auto inIX = [](auto a, auto l, auto r) -> bool { return (l <= a && a <  r); };
auto inXI = [](auto a, auto l, auto r) -> bool { return (l <  a && a <= r); };
auto inXX = [](auto a, auto l, auto r) -> bool { return (l <  a && a <  r); };
auto setmin   = [](auto & a, auto b) -> bool { return (b <  a ? a = b, true : false); };
auto setmax   = [](auto & a, auto b) -> bool { return (b >  a ? a = b, true : false); };
auto setmineq = [](auto & a, auto b) -> bool { return (b <= a ? a = b, true : false); };
auto setmaxeq = [](auto & a, auto b) -> bool { return (b >= a ? a = b, true : false); };
using LL = long long int;
using LD = long double;
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define MT make_tuple
#define FI first
#define SE second
#define FR front()
#define BA back()
#define ALL(a) begin(a), end(a)
#define RALL(a) rbegin(a), rend(a)
#define RV(a) reverse(ALL(a))
#define ST(a) sort(ALL(a))
#define RST(a) sort(RALL(a))
#define SC static_cast
#define SI(a) SC<int>(a.size())
#define SL(a) SC<LL>(a.size())
#define RF(e, ...) for(auto && e: __VA_ARGS__)
#define SF(a, ...) for(auto && [__VA_ARGS__]: a)
#define until(...) while(not(__VA_ARGS__))
#define if_not(...) if(not(__VA_ARGS__))
#define ef else if
#define UR assert(false)
auto * IS = & cin;
auto * OS = & cout;
template<typename ... A> void in(A & ... a) { (* IS >> ... >> a); }
#define IN(...) __VA_ARGS__; in(__VA_ARGS__)
struct OS_init { OS_init() { * OS << boolalpha << fixed << setprecision(20); } } os_init_;
void                                      out_([[maybe_unused]] string const & s) { }
template<typename A                > void out_([[maybe_unused]] string const & s, A const & a) { * OS << a; }
template<typename A, typename ... B> void out_(                 string const & s, A const & a, B const & ... b) { * OS << a << s; out_(s, b ...); }
auto outF  = [](string const & s, string const & t, auto const & ... a) { out_(s, a ...); * OS << t << flush; };
auto outN  = [](auto const & ... a) { outF(""  , ""  , a ...); };
auto outS  = [](auto const & ... a) { outF(" " , " " , a ...); };
auto outL  = [](auto const & ... a) { outF("\n", "\n", a ...); };
auto outSN = [](auto const & ... a) { outF(" " , ""  , a ...); };
auto outNL = [](auto const & ... a) { outF(""  , "\n", a ...); };
auto outSL = [](auto const & ... a) { outF(" " , "\n", a ...); };
auto out   = outSL;
template<typename A                > void disp_(A const & a) { * OS << a; }
template<typename A, typename ... T> void disp_(A const & a, string const & s, T const & ... t) { string ss; for(auto && e: a) { * OS << ss; ss = s; disp_(e, t ...); } }
auto dispI = [](auto const & a, auto const & s, auto const & ... t) { disp_(a, t ...); * OS << s << flush; };
auto dispT = [](auto const & a, auto const & s, auto const & ... t) { for(auto && e: a) { disp_(e, t ...); * OS << s; } * OS << flush; };
auto dispL = [](auto const & a,                 auto const & ... t) { dispT(a, "\n", t ...); };
template<typename A> istream & operator>>(istream & is, vector<A>       & v) { for(auto && e: v) { is >> e; } return is; }
template<typename A> ostream & operator<<(ostream & os, vector<A> const & v) { string ss; for(auto && e: v) { os << ss << e; ss = " "; } return os; }
template<typename A                > auto make_v(A a) { return a; }
template<typename A, typename ... M> auto make_v(A a, int n, M ... m) { return vector(n, make_v(a, m ...)); }
template<typename A, typename ... N> auto read_v(N ... n) { auto a = make_v(A { }, n ...); in(a); return a; }
template<typename A, size_t N> istream & operator>>(istream & is, array<A, N>       & a) { for(auto && e: a) { is >> e; } return is; }
template<typename A, size_t N> ostream & operator<<(ostream & os, array<A, N> const & a) { string ss; for(auto && e: a) { os << ss << e; ss = " "; } return os; }
template<typename A, typename B> istream & operator>>(istream & is, pair<A, B>       & p) { return is >> p.first >> p.second; }
template<typename A, typename B> ostream & operator<<(ostream & os, pair<A, B> const & p) { return os << p.first << " " << p.second; }
template<int I = 0, typename T> void tin_ (istream & is, T       & t) { if constexpr(I < tuple_size<T>::value) { is >> get<I>(t); tin_<I + 1>(is, t); } }
template<int I = 0, typename T> void tout_(ostream & os, T const & t) { if constexpr(I < tuple_size<T>::value) { if(I != 0) { os << " "; } os << get<I>(t); tout_<I + 1>(os, t); } }
template<typename ... A> istream & operator>>(istream & is, tuple<A ...>       & t) { tin_ (is, t); return is; }
template<typename ... A> ostream & operator<<(ostream & os, tuple<A ...> const & t) { tout_(os, t); return os; }

// ---- ----

template<typename T, T(* PLUS)(T, T), T(* MULT)(T, T), T(* ZERO)(), T(* UNIT)()> struct Matrix_ {
	int h, w;
	vector<vector<T>> v;
	explicit Matrix_(int h = 1):    h(h), w(h), v(h, vector<T>(w, ZERO())) { }
	explicit Matrix_(int h, int w): h(h), w(w), v(h, vector<T>(w, ZERO())) { }
	Matrix_(vector<vector<T>> const & v): h(SI(v)), w(SI(v[0])), v(v) {
		inc(i, h) { assert(SI(v[i]) == w); }
	}
	vector<T> const & operator[](int i) const { return v.at(i); }
	vector<T>       & operator[](int i)       { return v.at(i); }
	static Matrix_ unit(int n) {
		Matrix_ a(n);
		inc(i, n) { a[i][i] = UNIT(); }
		return a;
	}
	friend Matrix_ operator*(Matrix_ const & a, Matrix_ const & b) {
		assert(a.w == b.h);
		Matrix_ c(a.h, b.w);
		inc(i, a.h) {
		inc(j, b.w) {
		inc(k, a.w) {
			c[i][j] = PLUS(c[i][j], MULT(a[i][k], b[k][j]));
		}
		}
		}
		return c;
	}
	friend Matrix_ operator^(Matrix_ a, LL b) {
		assert(a.h == a.w);
		assert(b >= 0);
		auto p = Matrix_::unit(a.h);
		while(b) {
			if(b & 1) { p *= a; }
			a *= a;
			b >>= 1;
		}
		return p;
	}
	friend Matrix_ & operator*=(Matrix_ & a, Matrix_ const & b) { return (a = a * b); }
	friend Matrix_ & operator^=(Matrix_ & a, LL              b) { return (a = a ^ b); }
	friend Matrix_ & operator*=(Matrix_ & a, T b) {
		inc(i, a.h) {
		inc(j, a.w) {
			a[i][j] = MULT(a[i][j], b);
		}
		}
		return a;
	}
	friend Matrix_ operator*(Matrix_ a, T b) { return (a *= b); }
	friend Matrix_ operator*(T b, Matrix_ a) { return (a *= b); }
	friend ostream & operator<<(ostream & s, Matrix_ const & a) {
		inc(i, a.h) { s << a[i] << endl; }
		return s;
	}
};
template<typename T> T PLUS(T a, T b) { return a + b; };
template<typename T> T MULT(T a, T b) { return a * b; };
template<typename T> T ZERO() { return 0; };
template<typename T> T UNIT() { return 1; };
template<typename T> using Matrix = Matrix_<T, PLUS<T>, MULT<T>, ZERO<T>, UNIT<T>>;

// ----

template<LL M> class ModInt {
private:
	LL v;
	pair<LL, LL> ext_gcd(LL a, LL b) {
		if(b == 0) { assert(a == 1); return { 1, 0 }; }
		auto p = ext_gcd(b, a % b);
		return { p.SE, p.FI - (a / b) * p.SE };
	}
public:
	ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } }
	LL val() { return v; }
	static LL mod() { return M; }
	ModInt inv() { return ext_gcd(M, v).SE; }
	ModInt exp(LL b) {
		ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; }
		while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; }
		return p;
	}
	friend bool      operator< (ModInt    a, ModInt   b) { return (a.v <  b.v); }
	friend bool      operator> (ModInt    a, ModInt   b) { return (a.v >  b.v); }
	friend bool      operator<=(ModInt    a, ModInt   b) { return (a.v <= b.v); }
	friend bool      operator>=(ModInt    a, ModInt   b) { return (a.v >= b.v); }
	friend bool      operator==(ModInt    a, ModInt   b) { return (a.v == b.v); }
	friend bool      operator!=(ModInt    a, ModInt   b) { return (a.v != b.v); }
	friend ModInt    operator+ (ModInt    a            ) { return ModInt(+a.v); }
	friend ModInt    operator- (ModInt    a            ) { return ModInt(-a.v); }
	friend ModInt    operator+ (ModInt    a, ModInt   b) { return ModInt(a.v + b.v); }
	friend ModInt    operator- (ModInt    a, ModInt   b) { return ModInt(a.v - b.v); }
	friend ModInt    operator* (ModInt    a, ModInt   b) { return ModInt(a.v * b.v); }
	friend ModInt    operator/ (ModInt    a, ModInt   b) { return a * b.inv(); }
	friend ModInt    operator^ (ModInt    a, LL       b) { return a.exp(b); }
	friend ModInt  & operator+=(ModInt  & a, ModInt   b) { return (a = a + b); }
	friend ModInt  & operator-=(ModInt  & a, ModInt   b) { return (a = a - b); }
	friend ModInt  & operator*=(ModInt  & a, ModInt   b) { return (a = a * b); }
	friend ModInt  & operator/=(ModInt  & a, ModInt   b) { return (a = a / b); }
	friend ModInt  & operator^=(ModInt  & a, LL       b) { return (a = a ^ b); }
	friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; }
	friend ostream & operator<<(ostream & s, ModInt   b) { return (s << b.v); }
};
using MI = ModInt<10000>;

// ----

class Loop {
private:
	LL n, s; // v[n] == v[s] (s < n)
public:
	Loop(LL nn, LL ss) : n(nn), s(ss) { assert(inIX(s, 0, n)); }
	LL index(LL i) {
		assert(i >= 0);
		return (i < s ? i : s + (i - s) % (n - s));
	}
	LL count(LL k, LL i) { // # { x in [0, k) | index(x) == i }
		assert(inIX(i, 0, n));
		if(min(k, i) < s) { return (i < k ? 1 : 0); }
		i -= s;
		k -= s;
		return k / (n - s) + (i < k % (n - s) ? 1 : 0);
	}
};

int main() {
	LL IN(s, m, l);
	
	map<MI, int> mp;
	vector<MI> v;
	v.PB(s);
	mp[s] = 0;
	int p = -1;
	while(true) {
		MI x = (Matrix<MI>({ { v.BA, 1 }, { 1, 0 } }) ^ m)[1][0] - (m % 2);
		if(mp.count(x) == 1) { p = mp[x]; break; }
		mp[x] = SI(v);
		v.PB(x);
	}
	
	string ans = to_string(v[Loop(SI(v), p).index(l)].val());
	out(string(4 - SI(ans), '0') + ans);
}

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結果

テストケース

ソースコード